Skip to main content

Local Cohomology Using Macaulay2

  • Chapter
  • First Online:
Monomial Ideals, Computations and Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2083))

Abstract

Over the last 20 years there were many advances made in the computational theory of D-modules. Nowadays, the most common computer algebra systems such as Macaulay2 or Singular have important available packages for working with D-modules. In particular, the package D-modules [127] for Macaulay 2 [80] developed by A. Leykin and H. Tsai contains an implementation of the algorithms given by U. Walther [194] and T. Oaku and N.

Josep Àlvarez Montaner was partially supported by SGR2009-1284 and MTM2010-20279- C02-01.

Oscar Fernández-Ramos was partially supported by MTM2010-20279-C02-02.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    CoCoA is still working on that.

References

  1. J. Àlvarez Montaner, A. Leykin, Computing the support of local cohomology modules. J. Symb. Comput. 41, 1328–1344 (2006)

    Article  MATH  Google Scholar 

  2. F. Barkats, Calcul effectif de groupes de cohomologie locale à support dans des idéaux monomiaux. Ph.D. Thesis, Univ. Nice-Sophia Antipolis, 1995

    Google Scholar 

  3. D. Grayson, M. Stillman, Macaulay2, A software system for research in algebraic geometry (2011). Available at: http://www.math.uiuc.edu/Macaulay2

  4. A. Leykin, D-modules for Macaulay 2, in Mathematical Software: ICMS 2002 (World Scientific, Singapore, 2002), pp. 169–179

    Google Scholar 

  5. A. Leykin, M. Stillman, H. Tsai, D-modules for Macaulay 2 (2011). Available at: http://people.math.gatech.edu/~aleykin3/Dmodules

  6. T. Oaku, N. Takayama, Algorithms for D-modules—restriction, tensor product, localization, and local cohomology groups. J. Pure Appl. Algebra 156, 267–308 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Velasco, Minimal free resolutions that are not supported by a CW-complex. J. Algebra 319, 102–114 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. U. Walther, Algorithmic computation of local cohomology modules and the cohomological dimension of algebraic varieties. J. Pure Appl. Algebra 139, 303–321 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  9. U. Walther, D-modules and cohomology of varieties, in Computations in Algebraic Geometry with Macaulay 2. Algorithms and Computations in Mathematics, vol. 8 (Springer, Berlin, 2002), pp. 281–323

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Josep Àlvarez Montaner .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Montaner, J.À., Fernández-Ramos, O. (2013). Local Cohomology Using Macaulay2. In: Bigatti, A., Gimenez, P., Sáenz-de-Cabezón, E. (eds) Monomial Ideals, Computations and Applications. Lecture Notes in Mathematics, vol 2083. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38742-5_6

Download citation

Publish with us

Policies and ethics